Question: A guest brought us a bunch of flowers on Shabbos. What could we have done with them?
Answer: The Rema (OC 336:11) writes that one may place branches and flowers in water on Shabbos only if there are no flowers that will open up as a result. The Mishna Berura (336:54) clarifies that this only applies to branches and flowers that were already in and had fallen out. One cannot add any new flowers or water to the vase, though.
He writes (Shaar Hatziyun 336:48) that if necessary, one may rely on the Pri Megadim (Eshel Avraham 336:13) and Shulchan Aruch Harav (OC 336:18) who allow one to place a fresh bouquet of flowers in a vase on Shabbos providing that the flowers had fully opened and the water had been filled before Shabbos. Thus, one who had forgotten to place them in the vase before Shabbos would be allowed to add them to an existing vase of flowers (See Shemiras Shabbos Kehilchasa 26:26; n91).
Providing the flowers were picked before Shabbos, they are not muktze as they were picked for a bouquet. Thus, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchas 26:25) writes that a vase containing flowers is not muktze and may be moved on Shabbos. Likewise, one may remove flowers from a vase on Shabbos (See Rivevos Ephraim 1:258).
R’ Yosef Shalom Elyashiv (Dirshu Mishna Berura 336:n48) notes, though, that if the flowers haven’t fully opened, one must be careful when moving the vase not to shake the water around which could aid their growth.
In conclusion, one may gently move a vase with flowers and remove flowers from water, though one may only put flowers into that water if they have fully opened. No water may be added on Shabbos. Otherwise, one should place them into an empty vase.